(2x+6)(-4x+8)=0

Solution for (2x+6)(-4x+8)=0 equation:

(2x+6)(-4x+8)=0

We multiply parentheses ..

(-8x^2+16x-24x+48)=0

We get rid of parentheses

-8x^2+16x-24x+48=0

We add all the numbers together, and all the variables

-8x^2-8x+48=0

a = -8; b = -8; c = +48;
Δ = b2-4ac
Δ = -82-4·(-8)·48
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-40}{2*-8}=\frac{-32}{-16}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+40}{2*-8}=\frac{48}{-16}
=-3
$